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Simplifying 4.9t2 + 15.0t + -61.5 = 0 Reorder the terms: -61.5 + 15.0t + 4.9t2 = 0 Solving -61.5 + 15.0t + 4.9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -12.55102041 + 3.06122449t + t2 = 0 Move the constant term to the right: Add '12.55102041' to each side of the equation. -12.55102041 + 3.06122449t + 12.55102041 + t2 = 0 + 12.55102041 Reorder the terms: -12.55102041 + 12.55102041 + 3.06122449t + t2 = 0 + 12.55102041 Combine like terms: -12.55102041 + 12.55102041 = 0.00000000 0.00000000 + 3.06122449t + t2 = 0 + 12.55102041 3.06122449t + t2 = 0 + 12.55102041 Combine like terms: 0 + 12.55102041 = 12.55102041 3.06122449t + t2 = 12.55102041 The t term is 3.06122449t. Take half its coefficient (1.530612245). Square it (2.342773845) and add it to both sides. Add '2.342773845' to each side of the equation. 3.06122449t + 2.342773845 + t2 = 12.55102041 + 2.342773845 Reorder the terms: 2.342773845 + 3.06122449t + t2 = 12.55102041 + 2.342773845 Combine like terms: 12.55102041 + 2.342773845 = 14.893794255 2.342773845 + 3.06122449t + t2 = 14.893794255 Factor a perfect square on the left side: (t + 1.530612245)(t + 1.530612245) = 14.893794255 Calculate the square root of the right side: 3.859247887 Break this problem into two subproblems by setting (t + 1.530612245) equal to 3.859247887 and -3.859247887.Subproblem 1
t + 1.530612245 = 3.859247887 Simplifying t + 1.530612245 = 3.859247887 Reorder the terms: 1.530612245 + t = 3.859247887 Solving 1.530612245 + t = 3.859247887 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.530612245' to each side of the equation. 1.530612245 + -1.530612245 + t = 3.859247887 + -1.530612245 Combine like terms: 1.530612245 + -1.530612245 = 0.000000000 0.000000000 + t = 3.859247887 + -1.530612245 t = 3.859247887 + -1.530612245 Combine like terms: 3.859247887 + -1.530612245 = 2.328635642 t = 2.328635642 Simplifying t = 2.328635642Subproblem 2
t + 1.530612245 = -3.859247887 Simplifying t + 1.530612245 = -3.859247887 Reorder the terms: 1.530612245 + t = -3.859247887 Solving 1.530612245 + t = -3.859247887 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.530612245' to each side of the equation. 1.530612245 + -1.530612245 + t = -3.859247887 + -1.530612245 Combine like terms: 1.530612245 + -1.530612245 = 0.000000000 0.000000000 + t = -3.859247887 + -1.530612245 t = -3.859247887 + -1.530612245 Combine like terms: -3.859247887 + -1.530612245 = -5.389860132 t = -5.389860132 Simplifying t = -5.389860132Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.328635642, -5.389860132}
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